Sidious wouldn't have died, heres my take on how it would go and the after effects if Anakin never arrived in the office.
Anakin never arrives at Palpatine's office, thus he kills Mace Windu with his superiority in the force. He then realizes that getting Anakin to be his apprentice is now impossible, and then executes Order 66 with jedi around the galaxy dying. The raid on the temple is led by a detactment of Palpatine's royal guard leading the 501st, though because of Anakin not leading the attack is considered somewhat of a failure. Only 3 survivors in the temple are left, and they are Anakin Skywalker, Cin Drallig and Shaak Ti the 3 leave the temple and link up with Bail Organa, Yoda and Obi-Wan.
Padme gives birth to Luke and Leia, and the jedi go into hiding as the Galactic Empire takes control of the galaxy and the jedi are considered traitors. A few years pass, Luke and Leia begin their jedi training while the Rebel Alliance fights against the Empire though they have more resources and ships to start with being that they had help from the jedi raiding several Imperial convoys and getting many planets to support them. At this point Palpatine has a new apprentice, named Darth Anubis who is a very powerful sith lord. The battle of Yavin is roughly the same, and they leave Yavin IV in search of a new base of operations.
Eventually they set up on Hoth, and the battle of hoth does take place however since the Rebel Alliance has more resources, they have heavy artillery and their snowspeeders to combat the AT-ATs. Blizzard force led by General Veers, is taking heavy loses but not before the shield generator is destroyed and Darth Anbuis lands. Only Anakin and Cin are in the base, Shaak Ti, Obi-Wan, Yoda, Padme, Luke, Han and Chewie are out in the galaxy doing other Rebel operations on other worlds. Darth Anbuis enters the hanger where Anakin and Cin engage the sith lord in a fierce duel, Cin attacking first before being kicked back.
Anubis then uses force lighting against Anakin but he blocks it with his saber, Cin comes back using force speed and drives back the sith lord with Anakin before they disarmed him. The battle of hoth is in the Rebellion's favor, and Anubis is taken into custody where Alliance High Command executes him shortly after. A few more years pass, Yoda dies and Luke and Anakin have reached their full potential becoming the most powerful force users in history. Palpatine senses the demise of his apprentice, and he knows that he will soon be next meanwhile the Rebels are preparing their attack on the 2nd death star.
It all pretty much goes the same like in the movie, its a trap and such however the strike team consists of Han, Cin, Chewie and Luke with a detachment of Rebel Specforce Wilderness Fighters. They defeat the legion of stormtroopers with the ewoks help, and blow the shield bunker using charges while Leia, Shaak Ti, and Obi-Wan are coordinating the fleet attack(the fleet being 5X larger then what it was in the movies). Anakin meanwhile lands aboard the 2nd death star, while the battle goes on and heads towards the throne room confronting Palpatine. In a fierce duel, Anakin soon overcomes Palpatine and kills him before escaping the death star as it is about to blow.
With the 2nd death star destroyed, the Rebel fleet engages the remaining and demoralized imperial fleet forcing them to retreat into hyperspace. The war continues on for another few more years, and then The New Republic is formed.
This post was suprisingly well thought-out, did this just come to you when you saw this thread or had you been thinking about it for a while?